We often face degrees in various areas of life and even in life. When it comes to meters square or cubic, it is told about number too in the second or third degree when we see designation very small or on the contrary big sizes, it is often used 10^n. And, of course, there is a set of formulas with participation of degrees. And what actions with degrees are possible and how them to consider?
Instruction
1. Let's begin with the bases, with definition. Degree is the work of equal multipliers. The multiplier is called by the basis, and by number of multipliers – an exponent. Action which is made with degree is called exponentiation. The exponent can be positive and negative, an integer or in fraction, rules of actions with degrees remain at the same time the same. If the degree basis - a negative number, and an exponent odd, then the result of exponentiation is negative, but if an exponent even, result, in independence of that, the negative or positive sign before the degree basis, always has a plus.
2. All properties which we will list now are valid for degrees with the identical basis. If the bases at degrees different, then it is possible to put or subtract only after exponentiation. Just as to increase and divide. Because exponentiation, according to an established order of performance of arithmetic actions, has a priority over multiplication and division and also addition and subtraction which are carried out in the last turn. And for change of this strict sequence of actions, there are brackets in which priority actions consist.
3. What special rules of arithmetic actions exist for degrees about the identical bases? Remember the following properties of degrees. If before you the work from two sedate expressions, for example a^n*a^m, then it is possible to put degrees, here so a^(n+m). Similarly work with private, but degrees will already read one of another. a^n/a^m = a^(n-m).
4. In a case when exponentiation of other degree (a^n) ^m is required, indicators of degrees are multiplied and we receive а^ (n*m).
5. The following important rule if the basis of degree it is possible to present works in the form, then we can transform expression from (a*b) ^n to a^n*b^n. It is similarly possible to transform fraction. (and / b) ^n = a^n/b^n.
6. Final manuals. In case the exponent zero, result of exponentiation always is unit. If exponent negative, then this fractional expression. That is a^-n = 1/a^n. And the latest if an exponent fractional, then extraction of a root as a^(n/m) = m√a^n is relevant here.